Suppose that the inverse scattering problem is understood as follows: given fixed-energy phase shifts, corresponding to an unknown potential q = q(r) from a certain class, for example, q ∈ L 1,1 , recover this potential. Then it is proved that the Newton-Sabatier (NS) procedure does not solve the above problem. It is not a valid inversion method, in the following sense: 1) it is not possible to...

In this work, we propose a semi-analytical solution for Simple Compartmental Models, more specifically the SIR Model. From system of ordinary differential equations itself, with change variable through an extended domain-based mapping, seek to build sharing solutions paths field function, generated by partial equation. Using characteristic method, obtain exact function in terms arbitrary whose ...

Several deenitions of universality of an n-point quadrature formula Q n are discussed. Universality means that Q n is able to compete with the respective optimal formula in many classes of functions. It is proved in a certain sense that the Gaus-sian quadrature formula satisses such a universality criterion. The underlying classes of functions are In each of these classes, we loose at most the ...

This paper outlines and qualitatively compares the implementations of seven different methods for solving Poisson’s equation on the disk. The methods include two classical finite elements, a cotan formula-based discrete differential geometry approach and four isogeometric constructions. The comparison reveals numerical convergence rates and, particularly for isogeometric constructions based on ...

In a previous paper it was shown how a probability measure (Eberlein measure) on the closed unit ball of the sequence space, h, can be used to find the variance a2 of the error functional for a quadrature formula for the fc-dimensional cube, regarded as a random variable. Here we give values of a for some specific formulae.

In this paper we are concerned with the estimation of integrals on the unit circle of the form ∫ 2π 0 f(eiθ)ω(θ)dθ by means of the so-called Szegö quadrature formulas, i.e., formulas of the type ∑n j=1 λjf(xj) with distinct nodes on the unit circle, exactly integrating Laurent polynomials in subspaces of dimension as high as possible. When considering certain weight functions ω(θ) related to th...

We provide an algorithm to compute arbitrarily many nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with complex poles outside [−1, 1]. Contrary to existing rational quadrature formulas, the computational effort is very low, even for extremely high degrees, and under certain conditions on the poles it can be shown that the c...

This paper extends some results for the weighted Moore–Penrose inverse A+M,N in Hilbert space to the so-called weighted Minkowski inverse A⊕M,N of an arbitrary rectangular matrix A ∈ Mm,n in Minkowski spaces μ. Four methods are also used for approximating the weighted Minkowski Inverse A⊕M,N . These methods are: Borel summable, Euler–Knopp summable, Newton–Raphson and Tikhonov’s methods. c © 20...

We give an explicit expression for the kernel of the error functional for Gaussian quadrature formulas with respect to weight functions of BernsteinSzegö type, i.e., weight functions of the form (1 x)"(l + x)ß /p(x), x e (-1, 1), where a, ß £ {-\,\} and p is a polynomial of arbitrary degree which is positive on [-1, 1]. With the help of this result the norm of the error functional can easily be...

Article history: Received 21 February 2013 Received in revised form 13 February 2014 Accepted 18 February 2014 Available online 19 March 2014